Abstract

A simplified approach is proposed to simulate the fluorescence signal from a fluorophore submerged inside a turbid medium using the Monte Carlo method. Based on the reversibility of photon propagation, the fluorescence signal can be obtained from a single Monte Carlo simulation of the excitation light. This is computationally less expensive and also allows for the direct use of well-validated nonfluorescence photon migration Monte Carlo codes. Fluorescence signals from a mouse tissuelike phantom were computed using both the simplified Monte Carlo simulation and the diffusion approximation. The relative difference of signal intensity was found to be at most 30% for a fluorophore placed in the medium at various depths and horizontally midway between a source–detector pair separated by 3  mm. The difference in time characteristics of the signal is also examined.

© 2007 Optical Society of America

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A. D. Klose, V. Ntziachristos, and A. H. Hielscher, "The inverse source problem based on the radiative transfer equation in optical molecular imaging," J. Comput. Phys. 202, 323-345 (2005).
[CrossRef]

K. Vishwanath and M. Mycek, "Time-resolved photon migration in bi-layered tissue models," Opt. Express 13, 7466-7482 (2005).
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A. Soubret, J. Ripoll, and V. Ntziachristos, "Accuracy of fluorescent tomography in the presence of heterogeneities: study of the normalized born ratio," IEEE Trans. Med. Imaging 24, 1377-1386 (2005).
[CrossRef] [PubMed]

K. Ren, B. Moa-Anderson, G. Bal, X. Gu, and A. H. Hielscher, "Frequency domain tomography in small animals with the equation of radiative transfer," in Optical Tomography and Spectroscopy of Tissue VI, B. Chance, R. R. Alfano, B. J. Tromberg, M. Tamura, and E. M. Sevick-Muraca, eds., Proc. SPIE 5693, 111-120 (2005).
[CrossRef]

G. Alexandrakis, F. R. Rannou, and A. F. Chatziioannou, "Tomographic bioluminescence imaging by use of a combined optical-PET (OPET) system: a computer simulation feasibility study," Phys. Med. Biol. 50, 4225-4241 (2005).
[CrossRef] [PubMed]

2004

Y. Phaneendra Kumar and R. M. Vasu, "Reconstruction of optical properties of low-scattering tissue using derivative estimated through perturbation Monte-Carlo method," J. Biomed. Opt. 9, 1002-1012 (2004).
[CrossRef] [PubMed]

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[CrossRef] [PubMed]

D. Hall, G. Ma, F. Lesage, and Y. Wang, "Simple time-domain optical method for estimating the depth and concentration of a fluorescent inclusion in a turbid medium," Opt. Lett. 29, 2258-2260 (2004).
[CrossRef] [PubMed]

2003

E. E. Graves, J. Ripoll, R. Weissleder, and V. Ntziachristos, "A submillimeter resolution fluorescence molecular imaging system for small animal imaging," Med. Phys. 30, 901-911 (2003).
[CrossRef] [PubMed]

A. B. Milstein, S. Oh, K. J. Webb, C. A. Bouman, Q. Zhang, D. A. Boas, and R. P. Millane, "Fluorescence optical tomography," Appl. Opt. 42, 3081-3094 (2003).
[CrossRef] [PubMed]

2002

V. Ntziachristos, C. Tung, C. Bremer, and R. Weissleder, "Fluorescence-mediated tomography resolves protease activity in vivo," Nat. Med. 8, 757-760 (2002).
[CrossRef] [PubMed]

K. Vishwanath, B. W. Pogue, and M.-A. Mycek, "Quantitative fluorescence lifetime spectroscopy in turbid media: comparison of theoretical, experimental and computational methods," Phys. Med. Biol. 47, 3387-3405 (2002).
[CrossRef] [PubMed]

D. A. Boas, J. P. Culver, J. J. Stott, and A. K. Dunn, "Three-dimensional Monte Carlo code for photon migration through complex heterogeneous media including the adult human head," Opt. Express 10, 159-170 (2002).
[PubMed]

2001

1999

1998

1997

B. B. Das, F. Liu, and R. R. Alfano, "Time-resolved fluorescence and photon migration studies in biomedical and model random media," Rep. Prog. Phys. 60, 227-292 (1997).
[CrossRef]

J. Chang, H. L. Graber, and R. L. Barbour, "Imaging of fluorescence in highly scattering media," IEEE Trans. Biomed. Eng. 44, 810-822 (1997).
[CrossRef] [PubMed]

D. Contini, F. Martelli, and G. Zaccanti, "Photon migration through a turbid slab described by a model based on diffusion approximation. I. Theory," Appl. Opt. 36, 4587-4599 (1997).
[CrossRef] [PubMed]

A. Kienle and M. S. Patterson, "Improved solutions of the steady-state and the time-resolved diffusion equations for reflectance from semi-infinite turbid medium," J. Opt. Soc. Am. A 14, 246-254 (1997).
[CrossRef]

1996

1995

L.-H. Wang, S. L. Jacques, and L.-Q. Zheng, "MCML--Monte Carlo modeling of photon transport in multilayered tissues," Comput. Methods Programs Biomed. 47, 131-146 (1995).
[CrossRef] [PubMed]

1994

1991

1989

1983

Adam, G.

B. C. Wilson and G. Adam, "A Monte Carlo model for the absorption and flux distribution of light in tissue," Med. Phys. 10, 824-830 (1983).
[CrossRef] [PubMed]

Alexandrakis, G.

G. Alexandrakis, F. R. Rannou, and A. F. Chatziioannou, "Tomographic bioluminescence imaging by use of a combined optical-PET (OPET) system: a computer simulation feasibility study," Phys. Med. Biol. 50, 4225-4241 (2005).
[CrossRef] [PubMed]

Alfano, R. R.

B. B. Das, F. Liu, and R. R. Alfano, "Time-resolved fluorescence and photon migration studies in biomedical and model random media," Rep. Prog. Phys. 60, 227-292 (1997).
[CrossRef]

Arridge, S. R.

S. R. Arridge, "Optical tomography in medical imaging," Inverse Probl. 15, R41-R93 (1999).
[CrossRef]

Bal, G.

K. Ren, B. Moa-Anderson, G. Bal, X. Gu, and A. H. Hielscher, "Frequency domain tomography in small animals with the equation of radiative transfer," in Optical Tomography and Spectroscopy of Tissue VI, B. Chance, R. R. Alfano, B. J. Tromberg, M. Tamura, and E. M. Sevick-Muraca, eds., Proc. SPIE 5693, 111-120 (2005).
[CrossRef]

Barbour, R. L.

J. Chang, H. L. Graber, and R. L. Barbour, "Imaging of fluorescence in highly scattering media," IEEE Trans. Biomed. Eng. 44, 810-822 (1997).
[CrossRef] [PubMed]

Belenkov, A.

P. Gallant, A. Belenkov, G. Ma, F. Lesage, Y. Wang, D. Hall, and L. McIntosh, "A quantitative time-domain optical imager for small animals in vivo fluorescence studies," in Biomedical Optics Topical Meeting on CD-ROM (Optical Society of America, 2004), paper WD2.

Bevilacqua, F.

Boas, D. A.

Bouman, C. A.

Bremer, C.

V. Ntziachristos, C. Tung, C. Bremer, and R. Weissleder, "Fluorescence-mediated tomography resolves protease activity in vivo," Nat. Med. 8, 757-760 (2002).
[CrossRef] [PubMed]

Burch, C. L.

Chance, B.

Chang, J.

J. Chang, H. L. Graber, and R. L. Barbour, "Imaging of fluorescence in highly scattering media," IEEE Trans. Biomed. Eng. 44, 810-822 (1997).
[CrossRef] [PubMed]

Chatziioannou, A. F.

G. Alexandrakis, F. R. Rannou, and A. F. Chatziioannou, "Tomographic bioluminescence imaging by use of a combined optical-PET (OPET) system: a computer simulation feasibility study," Phys. Med. Biol. 50, 4225-4241 (2005).
[CrossRef] [PubMed]

Cong, W. X.

H. Li, J. Tian, F. P. Zhu, W. X. Cong, L. V. Wang, E. A. Hoffman, and G. Wang, "A mouse optical simulation environment (MOSE) to investigate bioluminescent phenomena with the Monte Carlo method," Acad. Radiol. 11, 1029-1038 (2004).
[CrossRef] [PubMed]

Contini, D.

Culver, J. P.

Das, B. B.

B. B. Das, F. Liu, and R. R. Alfano, "Time-resolved fluorescence and photon migration studies in biomedical and model random media," Rep. Prog. Phys. 60, 227-292 (1997).
[CrossRef]

Dougherty, D. E.

Dunn, A. K.

Eppstein, M. J.

Feng, T.

Ferwerda, H. A.

Gallant, P.

P. Gallant, A. Belenkov, G. Ma, F. Lesage, Y. Wang, D. Hall, and L. McIntosh, "A quantitative time-domain optical imager for small animals in vivo fluorescence studies," in Biomedical Optics Topical Meeting on CD-ROM (Optical Society of America, 2004), paper WD2.

Graber, H. L.

J. Chang, H. L. Graber, and R. L. Barbour, "Imaging of fluorescence in highly scattering media," IEEE Trans. Biomed. Eng. 44, 810-822 (1997).
[CrossRef] [PubMed]

Graves, E. E.

E. E. Graves, J. Ripoll, R. Weissleder, and V. Ntziachristos, "A submillimeter resolution fluorescence molecular imaging system for small animal imaging," Med. Phys. 30, 901-911 (2003).
[CrossRef] [PubMed]

Groenhuis, R. A.

Gu, X.

K. Ren, B. Moa-Anderson, G. Bal, X. Gu, and A. H. Hielscher, "Frequency domain tomography in small animals with the equation of radiative transfer," in Optical Tomography and Spectroscopy of Tissue VI, B. Chance, R. R. Alfano, B. J. Tromberg, M. Tamura, and E. M. Sevick-Muraca, eds., Proc. SPIE 5693, 111-120 (2005).
[CrossRef]

Hall, D.

D. Hall, G. Ma, F. Lesage, and Y. Wang, "Simple time-domain optical method for estimating the depth and concentration of a fluorescent inclusion in a turbid medium," Opt. Lett. 29, 2258-2260 (2004).
[CrossRef] [PubMed]

P. Gallant, A. Belenkov, G. Ma, F. Lesage, Y. Wang, D. Hall, and L. McIntosh, "A quantitative time-domain optical imager for small animals in vivo fluorescence studies," in Biomedical Optics Topical Meeting on CD-ROM (Optical Society of America, 2004), paper WD2.

Haskell, R. C.

Hayakawa, C. K.

Hielscher, A. H.

K. Ren, B. Moa-Anderson, G. Bal, X. Gu, and A. H. Hielscher, "Frequency domain tomography in small animals with the equation of radiative transfer," in Optical Tomography and Spectroscopy of Tissue VI, B. Chance, R. R. Alfano, B. J. Tromberg, M. Tamura, and E. M. Sevick-Muraca, eds., Proc. SPIE 5693, 111-120 (2005).
[CrossRef]

A. D. Klose, V. Ntziachristos, and A. H. Hielscher, "The inverse source problem based on the radiative transfer equation in optical molecular imaging," J. Comput. Phys. 202, 323-345 (2005).
[CrossRef]

Hillman, E.

E. Hillman, "Experimental and theoretical investigations of near infrared tomographic imaging methods and clinical applications," Ph.D. dissertation (University of London, 2002).

Hoffman, E. A.

H. Li, J. Tian, F. P. Zhu, W. X. Cong, L. V. Wang, E. A. Hoffman, and G. Wang, "A mouse optical simulation environment (MOSE) to investigate bioluminescent phenomena with the Monte Carlo method," Acad. Radiol. 11, 1029-1038 (2004).
[CrossRef] [PubMed]

Ishimaru, A.

Jacques, S. L.

L.-H. Wang, S. L. Jacques, and L.-Q. Zheng, "MCML--Monte Carlo modeling of photon transport in multilayered tissues," Comput. Methods Programs Biomed. 47, 131-146 (1995).
[CrossRef] [PubMed]

Jiang, H. B.

Kienle, A.

Klose, A. D.

A. D. Klose, V. Ntziachristos, and A. H. Hielscher, "The inverse source problem based on the radiative transfer equation in optical molecular imaging," J. Comput. Phys. 202, 323-345 (2005).
[CrossRef]

Kumar, Y. Phaneendra

Y. Phaneendra Kumar and R. M. Vasu, "Reconstruction of optical properties of low-scattering tissue using derivative estimated through perturbation Monte-Carlo method," J. Biomed. Opt. 9, 1002-1012 (2004).
[CrossRef] [PubMed]

Lesage, F.

D. Hall, G. Ma, F. Lesage, and Y. Wang, "Simple time-domain optical method for estimating the depth and concentration of a fluorescent inclusion in a turbid medium," Opt. Lett. 29, 2258-2260 (2004).
[CrossRef] [PubMed]

P. Gallant, A. Belenkov, G. Ma, F. Lesage, Y. Wang, D. Hall, and L. McIntosh, "A quantitative time-domain optical imager for small animals in vivo fluorescence studies," in Biomedical Optics Topical Meeting on CD-ROM (Optical Society of America, 2004), paper WD2.

Li, H.

H. Li, J. Tian, F. P. Zhu, W. X. Cong, L. V. Wang, E. A. Hoffman, and G. Wang, "A mouse optical simulation environment (MOSE) to investigate bioluminescent phenomena with the Monte Carlo method," Acad. Radiol. 11, 1029-1038 (2004).
[CrossRef] [PubMed]

Li, X. D.

Liu, F.

B. B. Das, F. Liu, and R. R. Alfano, "Time-resolved fluorescence and photon migration studies in biomedical and model random media," Rep. Prog. Phys. 60, 227-292 (1997).
[CrossRef]

Ma, G.

D. Hall, G. Ma, F. Lesage, and Y. Wang, "Simple time-domain optical method for estimating the depth and concentration of a fluorescent inclusion in a turbid medium," Opt. Lett. 29, 2258-2260 (2004).
[CrossRef] [PubMed]

P. Gallant, A. Belenkov, G. Ma, F. Lesage, Y. Wang, D. Hall, and L. McIntosh, "A quantitative time-domain optical imager for small animals in vivo fluorescence studies," in Biomedical Optics Topical Meeting on CD-ROM (Optical Society of America, 2004), paper WD2.

Martelli, F.

McAdams, M. S.

McIntosh, L.

P. Gallant, A. Belenkov, G. Ma, F. Lesage, Y. Wang, D. Hall, and L. McIntosh, "A quantitative time-domain optical imager for small animals in vivo fluorescence studies," in Biomedical Optics Topical Meeting on CD-ROM (Optical Society of America, 2004), paper WD2.

Millane, R. P.

Milstein, A. B.

Moa-Anderson, B.

K. Ren, B. Moa-Anderson, G. Bal, X. Gu, and A. H. Hielscher, "Frequency domain tomography in small animals with the equation of radiative transfer," in Optical Tomography and Spectroscopy of Tissue VI, B. Chance, R. R. Alfano, B. J. Tromberg, M. Tamura, and E. M. Sevick-Muraca, eds., Proc. SPIE 5693, 111-120 (2005).
[CrossRef]

Mycek, M.

Mycek, M.-A.

K. Vishwanath, B. W. Pogue, and M.-A. Mycek, "Quantitative fluorescence lifetime spectroscopy in turbid media: comparison of theoretical, experimental and computational methods," Phys. Med. Biol. 47, 3387-3405 (2002).
[CrossRef] [PubMed]

Ntziachristos, V.

A. D. Klose, V. Ntziachristos, and A. H. Hielscher, "The inverse source problem based on the radiative transfer equation in optical molecular imaging," J. Comput. Phys. 202, 323-345 (2005).
[CrossRef]

A. Soubret, J. Ripoll, and V. Ntziachristos, "Accuracy of fluorescent tomography in the presence of heterogeneities: study of the normalized born ratio," IEEE Trans. Med. Imaging 24, 1377-1386 (2005).
[CrossRef] [PubMed]

E. E. Graves, J. Ripoll, R. Weissleder, and V. Ntziachristos, "A submillimeter resolution fluorescence molecular imaging system for small animal imaging," Med. Phys. 30, 901-911 (2003).
[CrossRef] [PubMed]

V. Ntziachristos, C. Tung, C. Bremer, and R. Weissleder, "Fluorescence-mediated tomography resolves protease activity in vivo," Nat. Med. 8, 757-760 (2002).
[CrossRef] [PubMed]

V. Ntziachristos and R. Weissleder, "Experimental three-dimensional fluorescence reconstruction of diffuse media using a normalized Born approximation," Opt. Lett. 26, 893-895 (2001).
[CrossRef]

Oh, S.

O'Leary, M. A.

Patterson, M. S.

Pogue, B.

Pogue, B. W.

K. Vishwanath, B. W. Pogue, and M.-A. Mycek, "Quantitative fluorescence lifetime spectroscopy in turbid media: comparison of theoretical, experimental and computational methods," Phys. Med. Biol. 47, 3387-3405 (2002).
[CrossRef] [PubMed]

Rannou, F. R.

G. Alexandrakis, F. R. Rannou, and A. F. Chatziioannou, "Tomographic bioluminescence imaging by use of a combined optical-PET (OPET) system: a computer simulation feasibility study," Phys. Med. Biol. 50, 4225-4241 (2005).
[CrossRef] [PubMed]

Ren, K.

K. Ren, B. Moa-Anderson, G. Bal, X. Gu, and A. H. Hielscher, "Frequency domain tomography in small animals with the equation of radiative transfer," in Optical Tomography and Spectroscopy of Tissue VI, B. Chance, R. R. Alfano, B. J. Tromberg, M. Tamura, and E. M. Sevick-Muraca, eds., Proc. SPIE 5693, 111-120 (2005).
[CrossRef]

Ripoll, J.

A. Soubret, J. Ripoll, and V. Ntziachristos, "Accuracy of fluorescent tomography in the presence of heterogeneities: study of the normalized born ratio," IEEE Trans. Med. Imaging 24, 1377-1386 (2005).
[CrossRef] [PubMed]

E. E. Graves, J. Ripoll, R. Weissleder, and V. Ntziachristos, "A submillimeter resolution fluorescence molecular imaging system for small animal imaging," Med. Phys. 30, 901-911 (2003).
[CrossRef] [PubMed]

Sevick-Muraca, E. M.

Soubret, A.

A. Soubret, J. Ripoll, and V. Ntziachristos, "Accuracy of fluorescent tomography in the presence of heterogeneities: study of the normalized born ratio," IEEE Trans. Med. Imaging 24, 1377-1386 (2005).
[CrossRef] [PubMed]

Spanier, J.

Stott, J. J.

Svaasand, L. O.

ten Bosch, J. J.

Tian, J.

H. Li, J. Tian, F. P. Zhu, W. X. Cong, L. V. Wang, E. A. Hoffman, and G. Wang, "A mouse optical simulation environment (MOSE) to investigate bioluminescent phenomena with the Monte Carlo method," Acad. Radiol. 11, 1029-1038 (2004).
[CrossRef] [PubMed]

Tromberg, B. J.

Troy, T. L.

Tsay, T.

Tung, C.

V. Ntziachristos, C. Tung, C. Bremer, and R. Weissleder, "Fluorescence-mediated tomography resolves protease activity in vivo," Nat. Med. 8, 757-760 (2002).
[CrossRef] [PubMed]

Vasu, R. M.

Y. Phaneendra Kumar and R. M. Vasu, "Reconstruction of optical properties of low-scattering tissue using derivative estimated through perturbation Monte-Carlo method," J. Biomed. Opt. 9, 1002-1012 (2004).
[CrossRef] [PubMed]

Venugopalan, V.

Vishwanath, K.

K. Vishwanath and M. Mycek, "Time-resolved photon migration in bi-layered tissue models," Opt. Express 13, 7466-7482 (2005).
[CrossRef] [PubMed]

K. Vishwanath, B. W. Pogue, and M.-A. Mycek, "Quantitative fluorescence lifetime spectroscopy in turbid media: comparison of theoretical, experimental and computational methods," Phys. Med. Biol. 47, 3387-3405 (2002).
[CrossRef] [PubMed]

Wang, G.

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Figures (5)

Fig. 1
Fig. 1

Schematic of fluorescence spectroscopy in turbid medium such as biological tissue when reflection geometry is used.

Fig. 2
Fig. 2

(Color online) Comparison of the fluorescent intensity reaches the detector at (3, 0, 0) for a point fluorophore placed in a single pixel at various positions (x, z) in the x–z plane excited by a unitary impulse light source injected at (0, 0, 0) calculated by the simplified MC and the DA for the configuration geometry shown in Fig. 1.

Fig. 3
Fig. 3

(Color online) Fluorescence intensity calculated by the MC and the DA (upper panel) and the relative difference of the MC and the DA (lower panel) for a point fluorophore positioned horizontally midway between the source–detector pair at various depths inside the medium. The source–detector separation is 3 mm.

Fig. 4
Fig. 4

(Color online) TPSF from a fluorescence signal calculated by the MC and the DA for a point fluorophore positioned horizontally midway between the source–detector pair at depth z = 5.25   mm inside the medium. The source–detector separation is 3   mm .

Fig. 5
Fig. 5

(Color online) Time position of a fluorescence TPSF peak calculated by the MC and the DA (upper panel) and the difference of the MC and the DA (lower panel) for a point fluorophore positioned horizontally midway between the source–detector pair at various depths inside the medium. The source–detector separation is 3   mm .

Equations (11)

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F ( r , t ) = H x ( r r s , t ) [ i A i τ i exp ( t t τ i ) ] × E m ( r d r , t t ) S ( t t ) d t d t d t = H x ( r r s , t ) [ i A i τ i exp ( t τ i ) ] E m ( r d r , t ) S ( t ) ,
[ i A i τ i exp ( t τ i ) ] S ( t ) = 1 ,
F 0 ( r , t ) = H x ( r r s , t ) E m ( r d r , t ) .
F ( r , t ) = F 0 ( r , t ) [ i A i τ i exp ( t τ i ) ] S ( t ) .
Φ ( x , y , z , t ) = v exp ( μ a v t x 2 + y 2 4 D v t ) 4 π ( 4 π D v t ) 3 / 2 ×{ m = m = + exp [ ( z z + , m ) 2 4 D v t ] m = m = + exp [ ( z z , m ) 2 4 D v t ] } ,
z + , m = 2 m ( s + 2 z b ) + z 0 ,
z , m = 2 m ( s + 2 z b ) 2 z b z 0 ,
R eff = 1.440 n 2 + 0.710 n 1 + 0.668 + 0.0636 n
E m ( r d r , t ) = v exp ( μ a v t ( x d x ) 2 + ( y d y ) 2 4 D v t ) 4 π ( 4 π D v t ) 3 / 2 ×{ m = m = + exp [ ( z d z + , m e m ) 2 4 D v t ] m = m = + exp [ ( z d z , m e m ) 2 4 D v t ] } ,
z + , m e m = 2 m ( s + 2 z b ) + z ,
z , m e m = 2 m ( s + 2 z b ) 2 z b z

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